gpais

Gaussian Process Adaptive Importance Sampling

Topics

uncertainty_quantification

Specification

• Alias: gaussian_process_adaptive_importance_sampling

• Arguments: None

Child Keywords:

Required/Optional	Description of Group	Dakota Keyword	Dakota Keyword Description
Optional		build_samples	Number of initial model evaluations used in build phase
Optional		seed	Seed of the random number generator
Optional		samples_on_emulator	Number of samples at which to evaluate an emulator (surrogate)
Optional		import_build_points_file	File containing points you wish to use to build a surrogate
Optional		export_approx_points_file	Output file for surrogate model value evaluations
Optional		max_iterations	Number of iterations allowed for optimizers and adaptive UQ methods
Optional		response_levels	Values at which to estimate desired statistics for each response
Optional		probability_levels	Specify probability levels at which to estimate the corresponding response value
Optional		gen_reliability_levels	Specify generalized relability levels at which to estimate the corresponding response value
Optional		distribution	Selection of cumulative or complementary cumulative functions
Optional		rng	Selection of a random number generator
Optional		model_pointer	Identifier for model block to be used by a method

Description

gpais is recommended for problems that have a relatively small number of input variables (e.g. less than 10-20). This method, Gaussian Process Adaptive Importance Sampling, is outlined in the paper [DS14].

This method starts with an initial set of LHS samples and adds samples one at a time, with the goal of adaptively improving the estimate of the ideal importance density during the process. The approach uses a mixture of component densities. An iterative process is used to construct the sequence of improving component densities. At each iteration, a Gaussian process (GP) surrogate is used to help identify areas in the space where failure is likely to occur. The GPs are not used to directly calculate the failure probability; they are only used to approximate the importance density. Thus, the Gaussian process adaptive importance sampling algorithm overcomes limitations involving using a potentially inaccurate surrogate model directly in importance sampling calculations.